1. Field of the Invention
The invention relates to a fuzzy filtering method and associated fuzzy filter.
2. Discussion of the Related Art
As is known, a large number of mass-market applications (such as hi-fi, telecommunications) requires the definition of dedicated methods and architectures for filtering the deterministic signals corrupted by noise.
Traditionally, the problems of noise reduction ("denoising") are dealt with using linear filters (such as low-pass type filters with a fixed cut-off frequency) or with non-linear filters such as median filters.
The traditional linear filters are ideal for solving problems in which the frequency specifications are well defined. They do, however, have the disadvantage that, to reduce noise, they often eliminate data belonging to the original signal. As far as non-linear type filters are concerned, median filters have proved to be very efficient in eliminating pulse-type noise, but they are less efficient in the case of Gaussian noise.
For this reason, filters of a completely different type have been proposed: for instance, the article entitled "Fuzzy Rule-Based Signal Processing and Its Application to Image Restoration" by Kaoru Arakawa, IEEE Journal on Selected Areas in Communications, Vol. 12, No. 9, December 94, proposes a filter based on the processing of the signal by means of "fuzzy" logic, in which the signal is reconstructed by means of a filter which weighs local samples of the signal received and the weights are calculated using three rules whose variables are the difference between the signal samples, the time difference between those signal samples and the local variance of the signal. The filter also uses a learning signal to fix a number of filtering parameters.
This approach is burdensome in its calculations and is not always capable of supplying the desired accuracy of reconstruction of the signal.